4-methyl-1-pentene polymers are widely used in such applications as MWO food containers, syringes, analysis cells, experimental equipment such as beakers and flasks, base material used in preparing synthetic leathers in view of their high transparency and high melting point in the range of from 220 to 240.degree. C. and the resulting high heat distortion temperature. The 4-methyl-1-pentene polymers, however, were sometimes insufficient in other mechanical properties such as impact resistance, and the films made therefrom had insufficient heat sealability. A widely adopted solution for improving such insufficient heat sealability is addition of a low density polyethylene, an ethylene-propylene copolymer, or other ethylene-based resins. Such addition of the ethylene-based resin to the 4-methyl-1-pentene polymers have so far resulted in little improvement in their heat sealability, and instead, resulted in poor dispersion and deteriorated impact resistance. Another means proposed for improving the heat sealability of the films made from 4-methyl-1-pentene polymers is addition to the 4-methyl-1-pentene polymers of a particular propylene-.alpha.-olefin copolymer (JP-A-60-28442).
The films prepared by blending the 4-methyl-1-pentene polymers with the particular propylene-.alpha.-olefin copolymer were still insufficient both in their heat seal strength and improvement in mechanical properties. In view of such situation, there is a strong demand for a 4-methyl-1-pentene polymer composition which has improved heat sealability and mechanical properties while retaining the characteristic features of the 4-methyl-1-pentene polymer.